# What condition must be verified by the frequency so that an RC circuit acts as a differentiator? [closed]

So I am theoretically planning to make an RC differentiator circuit but I'm still a rookie with it so if someone can help me it would be appreciated.

• hint: What's the derivative of $A\sin\omega t$? And how would you express that in terms of things you can measure about the frequency response of a filter? Dec 9, 2019 at 19:44
• If you're familiar with transfer functions take a look at the transfer function of an ideal differentiator and compare it with the transfer function of your RC circuit and look for conditions that will make them approximately the same. Dec 9, 2019 at 19:50
• In case you're trying to build it in real life. Try to look up for "practical differentiator circuit". Such as this Texas Instruments guide: ti.com/lit/an/sboa276a/sboa276a.pdf Dec 9, 2019 at 20:50

The condition is defined by time domain exponential behavior and frequency domain.

You requirements must include some specification to be below some cutoff frequency or exponential constant T=RC with some tolerance such T defines the voltage decay to 64% of target.

e.g. differentiator for f < fo/10 or 20 dB down or T=1/fo=1/2piRC

The current phase leads voltage by 90 degrees.

e.g. a High Pass Filter performs differentiation (to some tolerance) below fo/10 typ.

A ideal differentiator has no upper limit in frequency gain +6dB/octave.

Other equivalent conditions to + 6dB/octave are +20dB/octave for the frequency range of interest.

## passive methods

a) It can block DC current with a series C with a shunt R
b) or shunt DC current to 0 volts with a series R and a shunt L.